Details

sample345.0ms

Algorithm

intervals

Results

240.0ms	150×	body	1280	valid
61.0ms	65×	body	640	valid
11.0ms	19×	body	320	valid
9.0ms	16×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

17.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series52.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
27.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
10×	`prod-diff`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `fma-neg` `diff-log` `associate-*l/` `flip--` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
7.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series58.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
18.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
27.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	463	864
1	1611	711
2	5001	708

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sin-cos-mult` `log1p-expm1-u`
3×	`*-commutative` `sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

5.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
9.0ms	(* (sin lambda1) (sin lambda2))
30.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
32.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	446	911
1	1954	729
2	5001	729

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(fma (sin lambda1) (cos lambda2) (- (* (cos lambda1) (sin lambda2))))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (sin lambda1) (cos lambda2) (- (* (cos lambda1) (sin lambda2))))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(fma (sin lambda1) (cos lambda2) (- (* (cos lambda1) (sin lambda2))))
31.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
31.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	379	830
1	1647	651
2	5001	651

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	29
1	42	29
2	42	29

end0.0ms

sample10.3s

Algorithm

intervals

Results

7.6s	4717×	body	1280	valid
1.8s	1883×	body	640	valid
354.0ms	550×	body	320	valid
119.0ms	637×	body	80	valid
86.0ms	213×	body	160	valid